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In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Under the assumption that each microstate is equally probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant.
The second law of thermodynamics states that the entropy of an isolated system never decreases. Such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that amount so that the total entropy increases. Entropy is a function of the state of the system, so the change in entropy of a system is determined by its initial and final states. In the idealization that a process is reversible, the entropy does not change, while irreversible processes always increase the total entropy.
Because it is determined by the number of random microstates, entropy is related to the amount of additional information needed to specify the exact physical state of a system, given its macroscopic specification. For this reason, it is often said that entropy is an expression of the disorder, or randomness of a system, or of the lack of information about it[citation needed]. The concept of entropy plays a central role in information theory.
Entropy is conserved for a reversible process. A reversible process is one that does not deviate from thermodynamic equilibrium, while producing the maximum work. Any process which happens quickly enough to deviate from thermal equilibrium cannot be reversible. In these cases energy is lost to heat, total entropy increases, and the potential for maximum work to be done in the transition is also lost. More specifically, total entropy is conserved in a reversible process and not conserved in an irreversible process. For example, in the Carnot cycle, while the heat flow from the hot reservoir to the cold reservoir represents an increase in entropy, the work output, if reversibly and perfectly stored in some energy storage mechanism, represents a decrease in entropy that could be used to operate the heat engine in reverse and return to the previous state, thus the total entropy change is still zero at all times if the entire process is reversible. An irreversible process increases entropy.